Question 1 :
In linear programming, lack of points for a solution set is said to
Question 3 :
What is the solution of $$x\le 4,y\ge 0$$ and $$x\le -4,y\le 0$$ ?
Question 4 :
If x + y = 3 and xy = 2, then the value of$$\displaystyle x^{3}-y^{3}$$ is equal to
Question 5 :
Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem (using simplex), we find that
Question 9 :
The corner points of the feasible region determined by the system of linear constraints are $$(0, 10),(5, 5), (25, 20)$$ and $$(0, 30)$$. Let $$Z = px + qy$$, where $$p, q > 0$$. Condition on $$p$$ and $$q$$ so that the maximum of $$Z$$ occurs at both the points $$(25, 20)$$ and $$(0, 30)$$is _______.
Question 10 : The given table shows the number of cars manufactured in four different colours on a particular day. Study it carefully and answer the question.<br/><table class="table table-bordered"><tbody><tr><td rowspan="2"> <b>Colour</b></td><td colspan="3"><b>   Number of cars manufactured</b></td></tr><tr><td><b> Vento</b></td><td><b> Creta</b></td><td><b>WagonR </b></td></tr><tr><td> Red</td><td> 65</td><td> 88</td><td> 93</td></tr><tr><td> White</td><td> 54</td><td> 42</td><td> 80</td></tr><tr><td> Black</td><td> 66</td><td> 52</td><td> 88</td></tr><tr><td> Sliver</td><td>37</td><td> 49</td><td> 74</td></tr></tbody></table>What was the total number of black cars manufactured?
Question 12 :
The number of points in $$\\ \left( -\infty ,\infty \right) $$ for which $${ x }^{ 2 }-x\sin { x } -\cos { x } =0$$, is
Question 13 :
A dealer wishes to purchase toys $$A$$ and $$B$$. He has Rs. $$580$$ and has space to store $$40$$ items. $$A$$ costs Rs. $$75$$ and $$B$$ costs Rs. $$90$$. He can make profit of Rs. $$10$$ and Rs.$$15$$ by selling $$A$$ and $$B$$ respectively assuming that he can sell all the items that he can buy formulation of this as L.P.P. is
Question 15 : <p>In graphical solutions of linear inequalities, solution can be divided into</p><ol></ol>
Question 16 :
To write the dual; it should be ensured that  <br/>I. All the primal variables are non-negative.<br/>II. All the bi values are non-negative.<br/>III. All the constraints are $$≤$$ type if it is maximization problem and $$≥$$ type if it is a minimization problem.
Question 17 :
In order to maximize the profit of the company, the optimal solution of which of the following equations is required?
Question 18 :
If $$x$$ is any real number, then which of the following is correct?
Question 19 :
Which of the following is an essential condition in a situation for linear programming to be useful?
Question 21 :
Apply linear programming to this problem. A firm wants to determine how many units of each of two products (products D and E) they should produce to make the most money. The profit in the manufacture of a unit of product D is $100 and the profit in the manufacture of a unit of product E is $87. The firm is limited by its total available labor hours and total available machine hours. The total labor hours per week are 4,000. Product D takes 5 hours per unit of labor and product E takes 7 hours per unit. The total machine hours are 5,000 per week. Product D takes 9 hours per unit of machine time and product E takes 3 hours per unit. Which of the following is one of the constraints for this linear program?
Question 22 :
If $$a,b,c \in +R$$ such that $$\lambda abc$$ is the minimum value of $$a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2)$$, then $$\lambda=$$
Question 23 :
Conclude from the following:<br/>$$n^2 > 10$$, and n is a positive integer.A: $$n^3$$B: $$50$$
Question 24 :
Find the output of the program given below if$$ x = 48$$<br/>and $$y = 60$$<br/>10  $$ READ x, y$$<br/>20  $$Let x = x/3$$<br/>30  $$ Let y = x + y + 8$$<br/>40  $$ z = \dfrac y4$$<br/>50  $$PRINT z$$<br/>60  $$End$$
Question 25 :
If $$x+y \leq 2, x\leq 0, y\leq 0$$ the point at which maximum value of $$3x+2y$$ attained will be.<br/>
